SUO: Re: Ontology
Cathy,
Thanks for the support.
Re semantic definition of truth: Hilpinen and Hintikka
pointed out that Peirce's "endoporeutic", which he
used to prove the soundness of his rules of inference
for existential graphs, was a version of Hintikka's
game-theoretical semantics, which is a more elegant
form of Tarski's model theory. See my commentary
to Peirce's MS 514 and the references listed there:
http://www.jfsowa.com/peirce/ms514.htm
Existential Graphs
I also include quotations that compare Ockham's
definitions to Peirce's and Tarski's. Despite his
use of Latin, Ockham's formulation was precise enough
to give Peirce an idea of how to apply the approach
to modern logic -- over 30 years before Tarski.
CL> I actually find the overall trajectory of his thought
> much more of a slow steady development than Russell's
> frequent changes of mind.
Yes. See J. A. Coffa, _The Semantic Tradition from
Kant to Carnap to the Vienna Station_, p. 106:
JAC> Whitehead is said to have commented that Russell was
> an entire Platonic dialogue in himself. The point was
> not that Russell's opinions changed through the years
> in dialectical fashion; this would not have been worth
> mentioning. Like every great philosopher, Russell
> felt the force of conflicting intuitions. Unlike most
> philosophers, he succumbed to those temptations without
> much regard to consistency.
The blurb on the back of Coffa's book, by the way, says
"Its history is meticulous." Yet it does not have a single
reference to Ockham or Peirce.
John
___________________________________________________________
> Hi Jay,
>
> You wrote:
>
>> Peirce had done what 'all'? Invented the Theory of
>> Types, for instance?
>> Found the conradiction in Frege? Invented the
>> semantical definition of
>> truth? Proved the Completeness Theorem? Invented
>> Godel numbering? Proved the
>> Incompleteness Theorem? None of these. Shall I
>> mention the Contradiction in
>> Frege again? There have been many developments in
>> logic since Peirce -- and
>> since Russell and Whitehead, for that matter.
>
> Not many people know this, but Peirce proved Cantor's
> famous result independently (using a version of the
> diagonalisation argument)!! The proofs are in a collection
> of Peirce's mathematical writings called "New Elements
> of Mathematics" (ed. Carolyn Eisele). When Peirce got wind
> of Cantor's work he read it thoroughly and sent him
> a series of excited letters trying to engage him
> in discussion but I think Cantor was too far gone
> at that stage in isolation/illness to really engage.
>
> As far as I understand it, Goedel's Incompleteness
> Proof relies crucially on the diagonalisation argument,
> so it wasn't too far off.
>
> Re. the contradiction in Frege, Peirce refused to call
> "Russell's Paradox" "Russell's Paradox" because he said
> it was only a trivial extension of ideas already expressed by Cantor.
>
> The issue of the semantic definition of truth is an
> interesting one. I have a feeling there might be
> something in Peirce along these lines, but I don't
> have any references to hand.
>
>> 'Anticipated in Latin' covers a multitude of sins.
>> Without the symbolic
>> logic -- variable binding quantifiers -- which
>> hadn't been invented, the
>> significance of Russell's analysis is lost.
>
>> I will mention once again that Peirce did not invent
>> the Theory of Types,
>> nor discover
>> the Contradiction. Nor invent set theory, for that
>> matter.
>
> There is a set theory in the "New Elements of Mathematics" also.
>
>> "Unfortunately Peirce was like Leibniz, not only in
>> his originality as a
>> logician, but also in his constitutional inability
>> to finish the many
>> projects he conceived." (P.410), Kneale and Kneale,
>> The Development of
>> Logic)
>
> I actually find the overall trajectory of his thought
> Much more of a slow steady development than Russell's
> frequent changes of mind.
>
>> "Working on some suggestions of De Morgan, Perice
>> explored this new field,
>> and shortly after the publication of the
>> Begriffschrift he even produced
>> independently a doctrine of functions with a
>> notation adequate for
>> expressing all the principles formulated by Frege;
>> but he never reduced his
>> thoughts to a system nor set out a number of basic
>> principles like those
>> given [by Frege]. (P. 510, Kneale and Kneale, The
>> Development of Logic)
>
> Again, the "New Elements of Mathematics" gives the
> lie to this statement. Check out Peirce's
> Existential Graphs, for instance.
>
>>[...]But your`s is very much a
>> minority opinion, as Google,
>> for instance, demonstrates: "Bertrand Russell" -
>> 236,000; "Charles Peirce" -
>> 6,250. (Unsurprisingly, neither one compares well
>> with "Bill Gates" -
>> 2,270,000).
>
> Is this meant to be an argument?
>
> Best regards,
> Cathy.
>